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000763348 020__ $$a9783319425450$$q(electronic book)
000763348 020__ $$a3319425455$$q(electronic book)
000763348 020__ $$z9783319425436
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000763348 049__ $$aISEA
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000763348 24504 $$aThe structure and stability of persistence modules /$$cFrédéric Chazal, Vin de Silva, Marc Glisse, Steve Oudot.
000763348 264_1 $$aSwitzerland :$$bSpringer,$$c2016.
000763348 300__ $$a1 online resource :$$billustrations.
000763348 336__ $$atext$$btxt$$2rdacontent
000763348 337__ $$acomputer$$bc$$2rdamedia
000763348 338__ $$aonline resource$$bcr$$2rdacarrier
000763348 4901_ $$aSpringerBriefs in mathematics,$$x2191-8198
000763348 504__ $$aIncludes bibliographical references and index.
000763348 5050_ $$aPreface; Acknowledgments; Contents; 1 Introduction; 1.1 A Brief History of Persistence; 1.2 Main Contributions; 1.3 Application: Stable Descriptors for Metric Spaces; 1.4 Application: Stable Clustering Using Persistence; 1.5 Recommended Reading; 1.6 Organisation; 1.7 Multisets; 2 Persistence Modules; 2.1 Persistence Modules Over a Real Parameter; 2.2 Index Posets; 2.3 Module Categories; 2.4 Interval Modules; 2.5 Interval Decomposition; 2.6 The Decomposition Persistence Diagram; 2.7 Quiver Calculations; 3 Rectangle Measures; 3.1 The Persistence Measure; 3.2 The Persistence Measure (Continued)
000763348 5058_ $$a3.3 Abstract r-Measures3.4 Equivalence of Measures and Diagrams; 3.5 Non-finite Measures; 3.6 Measures and Diagrams in the Extended Plane; 3.7 The Measure Persistence Diagram; 3.8 Tameness; 3.9 Tameness (Continued); 3.10 Vanishing Lemmas; 3.11 Vanishing Lemmas (Continued); 3.12 Finite Approximations; 4 Interleaving; 4.1 Shifted Homomorphisms; 4.2 Interleaving; 4.3 Interleaving (Continued); 4.4 The Interpolation Lemma; 4.5 The Interpolation Lemma (Continued); 5 The Isometry Theorem; 5.1 The Interleaving Distance; 5.2 The Bottleneck Distance; 5.3 The Bottleneck Distance (Continued)
000763348 5058_ $$a5.4 The Isometry Theorem5.5 The Converse Stability Theorem; 5.6 The Stability Theorem; 5.7 The Measure Stability Theorem; 5.8 The Measure Stability Theorem (Continued); 6 Variations; 6.1 Partial Interleavings; 6.2 Extended Persistence; References; Index
000763348 506__ $$aAccess limited to authorized users.
000763348 520__ $$aThis book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure and to establish the stability of such modules, providing a sound mathematical framework for the study of persistence diagrams. Completely self-contained, this brief introduces the notion of persistence measure and makes extensive use of a new calculus of quiver representations to facilitate explicit computations. Appealing to both beginners and experts in the subject, The Structure and Stability of Persistence Modules provides a purely algebraic presentation of persistence, and thus complements the existing literature, which focuses mainly on topological and algorithmic aspects.
000763348 588__ $$aDescription based on print version record.
000763348 650_0 $$aModules (Algebra)
000763348 7001_ $$aChazal, Frédéric,$$d1971-$$eauthor.
000763348 7001_ $$aDe Silva, Vin,$$d1971-$$eauthor.
000763348 7001_ $$aGlisse, Marc,$$eauthor.
000763348 7001_ $$aOudot, Steve Y.,$$d1979-$$eauthor.
000763348 77608 $$iPrint version:$$tStructure and Stability of Persistence Modules.$$d[Place of publication not identified] : Springer Verlag 2016$$z9783319425436$$w(OCoLC)952384117
000763348 830_0 $$aSpringerBriefs in mathematics.
000763348 852__ $$bebk
000763348 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-42545-0$$zOnline Access$$91397441.1
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000763348 980__ $$aEBOOK
000763348 980__ $$aBIB
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000763348 983__ $$aOnline
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